Find the solution to the following lhcc recurrence, confused!

ello ello!
I ran into this problem and i went in circles trying to figure it out. Anyone have any suggestions?
Here is what i have:
Find the solution to the following lhcc recurrence:
with initial conditions

The solution is of the form:
or suitable constants with
Find these constants.
[tex]r_1 = r_2 = \alpha_1 = \alpha_2 =[/tex]

Okay so I plugged the 2 inital conditions in for the solution form and got:
1 = [tex]\alpha_1[/tex] + [tex]\alpha_2[/tex]
4 = [tex]\alpha_1[/tex]*r1 + [tex]\alpha_2[/tex]*r2

I can't solve t hat, too many unkowns and not enough equations. I also tried to find a2,a3,a4, then putting it all in terms of a0 and a1, then i was like urnt, what now? THanks!

Thanks for the responce Tide but i'm still alittle lost.
I usually found the R's when they gave me an equation like r^2+4r+2 = 0, then just solve for r to find r1 and r2. How did u figure out r1 = 4 and r2 = 3?